The value of $k$ for which the lines $2 x + 3 y + a = 0$ and $5 x + k y + a = 0$ represent family of parallel lines is

3

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4.5

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7.5

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15

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Solution

The correct option is C $7.5$
Given lines are $2 x + 3 y + a = 0$ and $5 x + k y + a = 0$
Slope of parallel lines are equal,
Slope of first line is $\frac{- 2}{3}$
Slope of the second line is $\frac{- 5}{k}$
Equating both, we have

$- \frac{5}{k} = - \frac{2}{3}$

$⟹ k = 7.5$
Hence, option C is correct.

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